In the given figure “P” is a midpoint of BC, write the formula to find the co- ordinate of
P ?
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Given A △ABC in which P is the mid-point of BC, Q is the mid-point of BC, Q is the mid-point of AP, such that BQ produced meets AC at R
To prove RA=
3
1
CA
Construction Draw PS||BR, meeting AC at S.
Proof In △BCR, P is the mid-point of BC and PS||BR.
∴ S is the mid−point of CR.
⇒ CS=SR
In △APS, Q is the mid-point of AP and QR||PS.
∴ R is the mid−point of AS
⇒ AR=RS
From (i) and (ii), we get
AR=RS=SC
⇒ AC=AR+RS+SC=3AR
⇒ AR=
3
1
AC=
3
1
CA [Hence proved]
Step-by-step explanation:
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